feat: annotate conversations with model_provider for filtering (#5658)

Because conversations that use the Responses API can have encrypted
reasoning messages, trying to resume a conversation with a different
provider could lead to confusing "failed to decrypt" errors. (This is
reproducible by starting a conversation using ChatGPT login and resuming
it as a conversation that uses OpenAI models via Azure.)

This changes `ListConversationsParams` to take a `model_providers:
Option<Vec<String>>` and adds `model_provider` on each
`ConversationSummary` it returns so these cases can be disambiguated.

Note this ended up making changes to
`codex-rs/core/src/rollout/tests.rs` because it had a number of cases
where it expected `Some` for the value of `next_cursor`, but the list of
rollouts was complete, so according to this docstring:


bcd64c7e72/codex-rs/app-server-protocol/src/protocol.rs (L334-L337)

If there are no more items to return, then `next_cursor` should be
`None`. This PR updates that logic.






---
[//]: # (BEGIN SAPLING FOOTER)
Stack created with [Sapling](https://sapling-scm.com). Best reviewed
with [ReviewStack](https://reviewstack.dev/openai/codex/pull/5658).
* #5803
* #5793
* __->__ #5658

codex-rs/app-server/src/codex_message_processor.rs

@@ -827,19 +827,38 @@ impl CodexMessageProcessor {
         request_id: RequestId,
         params: ListConversationsParams,
     ) {
-        let page_size = params.page_size.unwrap_or(25);
+        let ListConversationsParams {
+            page_size,
+            cursor,
+            model_providers: model_provider,
+        } = params;
+        let page_size = page_size.unwrap_or(25);
         // Decode the optional cursor string to a Cursor via serde (Cursor implements Deserialize from string)
-        let cursor_obj: Option<RolloutCursor> = match params.cursor {
+        let cursor_obj: Option<RolloutCursor> = match cursor {
             Some(s) => serde_json::from_str::<RolloutCursor>(&format!("\"{s}\"")).ok(),
             None => None,
         };
         let cursor_ref = cursor_obj.as_ref();
+        let model_provider_filter = match model_provider {
+            Some(providers) => {
+                if providers.is_empty() {
+                    None
+                } else {
+                    Some(providers)
+                }
+            }
+            None => Some(vec![self.config.model_provider_id.clone()]),
+        };
+        let model_provider_slice = model_provider_filter.as_deref();
+        let fallback_provider = self.config.model_provider_id.clone();
 
         let page = match RolloutRecorder::list_conversations(
             &self.config.codex_home,
             page_size,
             cursor_ref,
             INTERACTIVE_SESSION_SOURCES,
+            model_provider_slice,
+            fallback_provider.as_str(),
         )
         .await
         {
@@ -858,7 +877,7 @@ impl CodexMessageProcessor {
         let items = page
             .items
             .into_iter()
-            .filter_map(|it| extract_conversation_summary(it.path, &it.head))
+            .filter_map(|it| extract_conversation_summary(it.path, &it.head, &fallback_provider))
             .collect();
 
         // Encode next_cursor as a plain string
@@ -1707,6 +1726,7 @@ async fn on_exec_approval_response(
 fn extract_conversation_summary(
     path: PathBuf,
     head: &[serde_json::Value],
+    fallback_provider: &str,
 ) -> Option<ConversationSummary> {
     let session_meta = match head.first() {
         Some(first_line) => serde_json::from_value::<SessionMeta>(first_line.clone()).ok()?,
@@ -1731,12 +1751,17 @@ fn extract_conversation_summary(
     } else {
         Some(session_meta.timestamp.clone())
     };
+    let conversation_id = session_meta.id;
+    let model_provider = session_meta
+        .model_provider
+        .unwrap_or_else(|| fallback_provider.to_string());
 
     Some(ConversationSummary {
-        conversation_id: session_meta.id,
+        conversation_id,
         timestamp,
         path,
         preview: preview.to_string(),
+        model_provider,
     })
 }
 
@@ -1760,7 +1785,8 @@ mod tests {
                 "cwd": "/",
                 "originator": "codex",
                 "cli_version": "0.0.0",
-                "instructions": null
+                "instructions": null,
+                "model_provider": "test-provider"
             }),
             json!({
                 "type": "message",
@@ -1780,7 +1806,8 @@ mod tests {
             }),
         ];
 
-        let summary = extract_conversation_summary(path.clone(), &head).expect("summary");
+        let summary =
+            extract_conversation_summary(path.clone(), &head, "test-provider").expect("summary");
 
         assert_eq!(summary.conversation_id, conversation_id);
         assert_eq!(
@@ -1789,6 +1816,7 @@ mod tests {
         );
         assert_eq!(summary.path, path);
         assert_eq!(summary.preview, "Count to 5");
+        assert_eq!(summary.model_provider, "test-provider");
         Ok(())
     }
 }